Feedback stabilization of a thermoacoustic device with experiments

Abstract

This paper deploys a recent mathematical tool to predict and prevent thermoacoustic instability (TAI) in a simple combustor. Widely-accepted characteristic of TAI is its time-delayed dynamics which originates from the acoustic coupling terms. Independently from the combustion instability studies, systems specialists have been developing mathematical approaches on similar time-delay problems. This document offers a bridge between the two veins of research. It utilizes the recent mathematical tool called the Cluster Treatment of Characteristic Roots (CTCR) to predict the onset of instability (TAI) for this simple benchmark combustor, Rijke Tube. Beyond prediction, for the operating conditions which already induce an undesirable TAI, this paper proposes a feedback controller design strategy which can recover stability. The suggested control logic is implemented on a test bed and the theoretical results are verified experimentally. c A s Q J F H G Y X

Stabilization of Unstable Second-Order Delay Plants under PID Control: A Nyquist Curve Analysis

“…Hwang applied the Ddecomposition approach to stabilize unstable first-order delay plants under PID control and constructed the complete set of stabilizing PID controller parameters [23]. In [24], Zalluhoglu et al utilized the CTCR method and obtained the stable region in the space of the control parameter. Based on the Nyquist stability criterion, Lee et al investigated the stabilization of a class of unstable all-pole delay plants of arbitrary order with a unstable pole and provided the maximum allowable time delay [25].…”

“…Due to the approximate substitution for the delay term, the method proposed in [11][12][13] is inadequately accurate. In contrast, the accurate approaches proposed in [20][21][22][23][24] are mathematically involved and do not provide an explicit characterization of the boundary of the feasible PID parameter region. Different from the previous works, we adopt the Nyquist curve analysis approach to achieve the feasible PID control parameter region, which provides an exact and explicit region and needs no complicated derivation.…”